git.distorted.org.uk Git - u/mdw/catacomb/blob - mpcrt.c

   1 /* -*-c-*-
   2  *
   3  * $Id$
   4  *
   5  * Chinese Remainder Theorem computations (Gauss's algorithm)
   6  *
   7  * (c) 1999 Straylight/Edgeware
   8  */
   9
  10 /*----- Licensing notice --------------------------------------------------*
  11  *
  12  * This file is part of Catacomb.
  13  *
  14  * Catacomb is free software; you can redistribute it and/or modify
  15  * it under the terms of the GNU Library General Public License as
  16  * published by the Free Software Foundation; either version 2 of the
  17  * License, or (at your option) any later version.
  18  *
  19  * Catacomb is distributed in the hope that it will be useful,
  20  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  21  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  22  * GNU Library General Public License for more details.
  23  *
  24  * You should have received a copy of the GNU Library General Public
  25  * License along with Catacomb; if not, write to the Free
  26  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  27  * MA 02111-1307, USA.
  28  */
  29
  30 /*----- Header files ------------------------------------------------------*/
  31
  32 #include "mp.h"
  33 #include "mpcrt.h"
  34 #include "mpmul.h"
  35 #include "mpbarrett.h"
  36
  37 /*----- Main code ---------------------------------------------------------*/
  38
  39 /* --- @mpcrt_create@ --- *
  40  *
  41  * Arguments:   @mpcrt *c@ = pointer to CRT context
  42  *              @mpcrt_mod *v@ = pointer to vector of moduli
  43  *              @size_t k@ = number of moduli
  44  *              @mp *n@ = product of all moduli (@MP_NEW@ if unknown)
  45  *
  46  * Returns:     ---
  47  *
  48  * Use:         Initializes a context for solving Chinese Remainder Theorem
  49  *              problems.  The vector of moduli can be incomplete.  Omitted
  50  *              items must be left as null pointers.  Not all combinations of
  51  *              missing things can be coped with, even if there is
  52  *              technically enough information to cope.  For example, if @n@
  53  *              is unspecified, all the @m@ values must be present, even if
  54  *              there is one modulus with both @m@ and @n@ (from which the
  55  *              product of all moduli could clearly be calculated).
  56  */
  57
  58 void mpcrt_create(mpcrt *c, mpcrt_mod *v, size_t k, mp *n)
  59 {
  60   size_t i;
  61
  62   /* --- Simple initialization things --- */
  63
  64   c->k = k;
  65   c->v = v;
  66
  67   /* --- Work out @n@ if I don't have it already --- */
  68
  69   if (n != MP_NEW)
  70     n = MP_COPY(n);
  71   else {
  72     mpmul mm;
  73     mpmul_init(&mm);
  74     for (i = 0; i < k; i++)
  75       mpmul_add(&mm, v[i].m);
  76     n = mpmul_done(&mm);
  77   }
  78
  79   /* --- A quick hack if %$k = 2$% --- */
  80
  81   if (k == 2) {
  82
  83     /* --- The %$n / n_i$% values are trivial in this case --- */
  84
  85     if (!v[0].n)
  86       v[0].n = MP_COPY(v[1].m);
  87     if (!v[1].n)
  88       v[1].n = MP_COPY(v[0].m);
  89
  90     /* --- Now sort out the inverses --- *
  91      *
  92      * @mp_gcd@ will ensure that the first argument is negative.
  93      */
  94
  95     if (!v[0].ni && !v[1].ni) {
  96       mp *g = MP_NEW;
  97       mp_gcd(&g, &v[0].ni, &v[1].ni, v[0].n, v[1].n);
  98       assert(MP_EQ(g, MP_ONE));
  99       mp_drop(g);
 100       v[0].ni = mp_add(v[0].ni, v[0].ni, v[1].n);
 101     } else {
 102       int i, j;
 103       mp *x;
 104
 105       if (!v[0].ni)
 106         i = 0, j = 1;
 107       else
 108         i = 1, j = 0;
 109
 110       x = mp_mul(MP_NEW, v[j].n, v[j].ni);
 111       x = mp_sub(x, x, MP_ONE);
 112       mp_div(&x, 0, x, v[i].n);
 113       v[i].ni = x;
 114     }
 115   }
 116
 117   /* --- Set up the Barrett context --- */
 118
 119   mpbarrett_create(&c->mb, n);
 120
 121   /* --- Walk through filling in @n@, @ni@ and @nnir@ --- */
 122
 123   for (i = 0; i < k; i++) {
 124     if (!v[i].n)
 125       mp_div(&v[i].n, 0, n, v[i].m);
 126     if (!v[i].ni)
 127       v[i].ni = mp_modinv(MP_NEW, v[i].n, v[i].m);
 128     if (!v[i].nni)
 129       v[i].nni = mp_mul(MP_NEW, v[i].n, v[i].ni);
 130   }
 131
 132   /* --- Done --- */
 133
 134   mp_drop(n);
 135 }
 136
 137 /* --- @mpcrt_destroy@ --- *
 138  *
 139  * Arguments:   @mpcrt *c@ - pointer to CRT context
 140  *
 141  * Returns:     ---
 142  *
 143  * Use:         Destroys a CRT context, releasing all the resources it holds.
 144  */
 145
 146 void mpcrt_destroy(mpcrt *c)
 147 {
 148   size_t i;
 149
 150   for (i = 0; i < c->k; i++) {
 151     if (c->v[i].m) mp_drop(c->v[i].m);
 152     if (c->v[i].n) mp_drop(c->v[i].n);
 153     if (c->v[i].ni) mp_drop(c->v[i].ni);
 154     if (c->v[i].nni) mp_drop(c->v[i].nni);
 155   }
 156   mpbarrett_destroy(&c->mb);
 157 }
 158
 159 /* --- @mpcrt_solve@ --- *
 160  *
 161  * Arguments:   @mpcrt *c@ = pointer to CRT context
 162  *              @mp *d@ = fake destination
 163  *              @mp **v@ = array of residues
 164  *
 165  * Returns:     The unique solution modulo the product of the individual
 166  *              moduli, which leaves the given residues.
 167  *
 168  * Use:         Constructs a result given its residue modulo an array of
 169  *              coprime integers.  This can be used to improve performance of
 170  *              RSA encryption or Blum-Blum-Shub generation if the factors
 171  *              of the modulus are known, since results can be computed mod
 172  *              each of the individual factors and then combined at the end.
 173  *              This is rather faster than doing the full-scale modular
 174  *              exponentiation.
 175  */
 176
 177 mp *mpcrt_solve(mpcrt *c, mp *d, mp **v)
 178 {
 179   mp *a = MP_ZERO;
 180   mp *x = MP_NEW;
 181   size_t i;
 182
 183   for (i = 0; i < c->k; i++) {
 184     x = mp_mul(x, c->v[i].nni, v[i]);
 185     x = mpbarrett_reduce(&c->mb, x, x);
 186     a = mp_add(a, a, x);
 187   }
 188   if (x)
 189     MP_DROP(x);
 190   a = mpbarrett_reduce(&c->mb, a, a);
 191   if (d != MP_NEW)
 192     MP_DROP(d);
 193   return (a);
 194 }
 195
 196 /*----- Test rig ----------------------------------------------------------*/
 197
 198 #ifdef TEST_RIG
 199
 200 static int verify(size_t n, dstr *v)
 201 {
 202   mpcrt_mod *m = xmalloc(n * sizeof(mpcrt_mod));
 203   mp **r = xmalloc(n * sizeof(mp *));
 204   mpcrt c;
 205   mp *a, *b;
 206   size_t i;
 207   int ok = 1;
 208
 209   for (i = 0; i < n; i++) {
 210     r[i] = *(mp **)v[2 * i].buf;
 211     m[i].m = *(mp **)v[2 * i + 1].buf;
 212     m[i].n = 0;
 213     m[i].ni = 0;
 214     m[i].nni = 0;
 215   }
 216   a = *(mp **)v[2 * n].buf;
 217
 218   mpcrt_create(&c, m, n, 0);
 219   b = mpcrt_solve(&c, MP_NEW, r);
 220
 221   if (!MP_EQ(a, b)) {
 222     fputs("\n*** failed\n", stderr);
 223     fputs("n = ", stderr);
 224     mp_writefile(c.mb.m, stderr, 10);
 225     for (i = 0; i < n; i++) {
 226       fprintf(stderr, "\nr[%u] = ", i);
 227       mp_writefile(r[i], stderr, 10);
 228       fprintf(stderr, "\nm[%u] = ", i);
 229       mp_writefile(m[i].m, stderr, 10);
 230       fprintf(stderr, "\nN[%u] = ", i);
 231       mp_writefile(m[i].n, stderr, 10);
 232       fprintf(stderr, "\nM[%u] = ", i);
 233       mp_writefile(m[i].ni, stderr, 10);
 234     }
 235     fputs("\nresult = ", stderr);
 236     mp_writefile(b, stderr, 10);
 237     fputs("\nexpect = ", stderr);
 238     mp_writefile(a, stderr, 10);
 239     fputc('\n', stderr);
 240     ok = 0;
 241   }
 242
 243   for (i = 0; i < n; i++)
 244     mp_drop(r[i]);
 245   mp_drop(a);
 246   mp_drop(b);
 247   mpcrt_destroy(&c);
 248   xfree(m);
 249   xfree(r);
 250   assert(mparena_count(MPARENA_GLOBAL) == 0);
 251   return (ok);
 252 }
 253
 254 static int crt1(dstr *v) { return verify(1, v); }
 255 static int crt2(dstr *v) { return verify(2, v); }
 256 static int crt3(dstr *v) { return verify(3, v); }
 257 static int crt4(dstr *v) { return verify(4, v); }
 258 static int crt5(dstr *v) { return verify(5, v); }
 259
 260 static test_chunk tests[] = {
 261   { "crt-1", crt1, { &type_mp, &type_mp,
 262                     &type_mp, 0 } },
 263   { "crt-2", crt2, { &type_mp, &type_mp,
 264                     &type_mp, &type_mp,
 265                     &type_mp, 0 } },
 266   { "crt-3", crt3, { &type_mp, &type_mp,
 267                     &type_mp, &type_mp,
 268                     &type_mp, &type_mp,
 269                     &type_mp, 0 } },
 270   { "crt-4", crt4, { &type_mp, &type_mp,
 271                     &type_mp, &type_mp,
 272                     &type_mp, &type_mp,
 273                     &type_mp, &type_mp,
 274                     &type_mp, 0 } },
 275   { "crt-5", crt5, { &type_mp, &type_mp,
 276                     &type_mp, &type_mp,
 277                     &type_mp, &type_mp,
 278                     &type_mp, &type_mp,
 279                     &type_mp, &type_mp,
 280                     &type_mp, 0 } },
 281   { 0, 0, { 0 } }
 282 };
 283
 284 int main(int argc, char *argv[])
 285 {
 286   sub_init();
 287   test_run(argc, argv, tests, SRCDIR "/tests/mpcrt");
 288   return (0);
 289 }
 290
 291 #endif
 292
 293 /*----- That's all, folks -------------------------------------------------*/